Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Journal of the Ramanujan Mathematical Society

Volume 38, Issue 1, March 2023  pp. 23–32.

Tilting correspondences of perfectoid rings

Authors:  Arnab Kundu
Author institution: Université Paris-Saclay, Laboratoire de Mathématiques d’Orsay, F-91405, Orsay, France.

Summary:  In this article, we present an alternate proof of a vanishing result of étale cohomology on perfectoid rings due to Cesnavicius and more recently proved by a different approach by Bhatt and Scholze. To establish that, we~prove a tilting equivalence of étale cohomology of perfectoid rings taking values in commutative, finite étale group schemes. On the way, we algebraically establish an analogue of the tilting correspondences of Scholze, between the category of finite étale schemes over a perfectoid ring and that over its tilt, without using tools from almost ring theory or adic spaces.

Contents   Full-Text PDF